CHAPTER 4
DISCOUNTED CASH FLOW
VALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
Assuming positive cash flows and interest rates, the future value increases and the present
value decreases.
2.
Assuming positive cash flows and interest rates, the present value will fall and the future
value will rise.
3.
The better deal is the one with equal installments.
4.
Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that
they are easier to compute, but, with modern computing equipment, that advantage is not
very important.
5.
A freshman does. The reason is that the freshman gets to use the money for much longer
before interest starts to accrue.
6.
It’s a reflection of the time value of money. GMAC gets to use the $500 immediately. If
GMAC uses it wisely, it will be worth more than $10,000 in thirty years.
7.
Oddly enough, it actually makes it more desirable since GMAC only has the right to pay the
full $10,000 before it is due. This is an example of a “call” feature. Such features are
discussed at length in a later chapter.
8.
The key considerations would be: (1) Is the rate of return implicit in the offer attractive
relative to other, similar risk investments? and (2) How risky is the investment; i.e., how
certain are we that we will actually get the $10,000? Thus, our answer does depend on who
is making the promise to repay.
9.
The Treasury security would have a somewhat higher price because the Treasury is the
strongest of all borrowers.
10.
The price would be higher because, as time passes, the price of the security will tend to rise
toward $10,000. This rise is just a reflection of the time value of money. As time passes, the
time until receipt of the $10,000 grows shorter, and the present value rises. In 2010, the price
will probably be higher for the same reason. We cannot be sure, however, because interest
rates could be much higher, or GMAC’s financial position could deteriorate. Either event
would tend to depress the security’s price.

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Solutions to Questions and Problems
NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require
multiple steps. Due to space and readability constraints, when these intermediate steps are
included in this solutions manual, rounding may appear to have occurred. However, the final
answer for each problem is found without rounding during any step in the problem.
Basic
1.
The simple interest per year is:
$5,000 × .07 = $350
So, after 10 years, you will have:
$350 × 10 = $3,500 in interest.
The total balance will be $5,000 + 3,500 = $8,500
With compound interest, we use the future value formula:
FV = PV(1 +
r
)
t
FV = $5,000(1.07)
10
= $9,835.76
The difference is:
$9,835.76 – 8,500 = $1,335.76
2.
To find the FV of a lump sum, we use:
FV = PV(1 +
r
)
t
a.
FV = $1,000(1.05)
10
= $1,628.89
b.
FV = $1,000(1.07)
10
= $1,967.15
c.
FV = $1,000(1.05)
20
= $2,653.30
d.
Because interest compounds on the interest already earned, the interest earned in part
c
is more than twice the interest earned in part
a
. With compound interest, future values
grow exponentially.

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